A CALM (catenary anchor leg mooring) system includes a buoy floating at the sea surface for connection to a vessel, and at least a few chains or lines extending in catenary curves from the buoy to locations spaced from one another on the seabed. Winds and currents that deflect the vessel and the buoy which holds it, cause one or more chains to be pulled more tautly while relieving tension in one or more other chains, to provide a restoring force that urges the buoy back to its initial quiescent position. While CALM systems operate effectively in deep waters, they can become ineffective in very shallow waters. In shallow waters, the chain which is pulled taut is not lifted much in average height, so that only a small amount of energy is available to restore the buoy to its initial position, and in addition the chain becomes taut after only a small buoy deflection. A mooring system of the CALM type which could operate even in relatively shallow waters to permit considerable buoy deflection and the application of large restoring forces through such deflection, would be of great value.